Introduction to Modified Gravity and Gravitational Alternative for Dark Energy

Abstract

We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of f(R), f(G) or f(R, G) gravity, model with non-linear gravitational coupling or string-inspired model with Gauss-Bonnet-dilaton coupling in the late universe where they lead to cosmic speed-up. It is shown that some of such theories may pass the Solar System tests. On the same time, it is demonstrated that they have quite rich cosmological structure: they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease. The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned. The late (phantom or quintessence) universe filled with dark fluid with inhomogeneous equation of state (where inhomogeneous terms are originated from the modified gravity) is also described.

Teleparallel dark energy with purely non-minimal coupling to gravity

“…Models with non-minimal derivative couplings have also been proposed [7]. For the second scenario a straightforward modification is to invoke a nonlinear function of the Ricci scalar in the gravity action to replace the linear function in GR, i.e., the f (R) theory [8] that can be regarded as one of the scalar-tensor theories. As to the change of the formalism, an example is teleparallel gravity that is formulated with torsion and a curvatureless connection.…”

Generalized teleparallel theory

“…We can now compare these equations with those obtained from f (R) gravity, whose equations of motion are [5][6][7][8][9] …”

“…This way to explain the accelerated expansion of our universe is known as modified or generalized gravity. Considering that the gravitational interaction is described only by the curvature of space-time, we can generalize the Einsteina e-mail: ednaldobarrosjr@gmail.com b e-mail: esialg@gmail.com Hilbert action through an analytic function of scalars of the theory, as for example f (R) gravities [5][6][7][8][9], withR being the Ricci scalar or curvature scalar, f (R, ) [10][11][12][13], with being the trace of energy-momentum tensor, or yet f (G) [14][15][16][17][18], f (R, G) [19][20][21][22][23][24] and f (R, ,R μν μν ) [25], with μν being the energy-momentum tensor.…”

Qualitative study in loop quantum cosmology

“…In particular, in a cosmological context, it was noticed that for the Friedmann-Lemaître-Robertson-Walker geometry, when the Equation of State (EoS) modeling the matter content was a linear equation with an EoS parameter greater than −1, a singularity named Big Bang appeared at early times, where the energy density of the universe diverges. Moreover, dealing with nonlinear EoS (see for instance, [1], where the analysis is done by expressing the EoS in the form of a power expansion), one can see that other kind of singularities such as Sudden singularity [2][3][4] or Big Freeze [5][6][7][8][9] appear.…”